Title: Steklov eigenvalues of hyperbolic manifolds with totally geodesic boundary
Abstract: The geometry and topology of closed negatively curved manifolds are subtly reflected in a geometric bound for the Laplace eigenvalues. In 1980, Schoen, Wolpert, and Yau showed that the small Laplace eigenvalues can be bounded from below and above by the length of a collection of closed simple geodesics cutting the surface into disjoint connected components. Schoen later obtained a spectral gap on negatively curved manifolds in higher dimensions which is in contrast with the result for hyperbolic surfaces. In this talk, we discuss how these results can be extended to the setting of the Steklov eigenvalue problem.
